## Brianna9898 2 years ago A floor has two square-shaped designs. The area of the second square-shaped design is nine times greater than the area of the first square-shaped design. Which statement gives the correct relationship between the lengths of the sides of the two squares?

1. Brianna9898

these are the options... The length of the side of the second square is 3 times greater than the length of the side of the first square. The length of the side of the second square is 12 times greater than the length of the side of the first square. The length of the side of the second square is 9 times greater than the length of the side of the first square. The length of the side of the second square is 6 times greater than the length of the side of the first square.

since $$A=l^2$$ and $$A'=l'^2$$ when $$A=9A'$$ sub them in to get the relationship between l and l'

3. Brianna9898

what am i supposed to sub in?

the l and l ' like this: $$A=9A'$$ $$l^2 = 9 l'^2$$

5. Brianna9898

im like really slow and have no idea wut im doing.-_-

lol. i guess i'll try to do it step by step. since $$A=l^2$$, $$A_1=l_1^2$$ (this is the first square)............(1) $$A_2=l_2^2$$ (this is the second square)........(2) since the area of the second square is nine times the first, (it's the only given condition, so we start from that.) $$A_2=9A_1$$ subbing (1) and (2) into it, we get, $$l_2^2=9l_1^2$$| what did you get after taking thesquare roots of both sides?

7. Brianna9898

sorry im back and thank you.

8. waterineyes

Just take the square root both the sides and tell us what you got as @Shadowys said above..

9. waterineyes

Getting ?? @Brianna9898

10. Brianna9898

I have no idea!

11. waterineyes

Are you getting till here" $l_2^2=9 l_1^2$

12. Brianna9898

why is there a 1 & 2 at the bottom

13. waterineyes

See when you will take square root you will get like: $\large \sqrt{l_2^2} = \sqrt{9 l_1^2}$ Can you tell what is this: $\large \sqrt{l_2^2} = ??$

14. Brianna9898

... and how am I supposed to square root an l ??

15. waterineyes

Oh that.. $$l_1$$ is showing length of first square. $$l_2$$ is for length of second square.

16. waterineyes

you can actually.. See, What is square root of this: $\large \sqrt{2^2} = ??$

17. Brianna9898

2

18. waterineyes

Similar way what will be square root of this: $\large \sqrt{l_2^2} = ??$

19. Brianna9898

$l$

20. Brianna9898

??

21. waterineyes

Or you can say $$l_2$$.. Good..

22. waterineyes

Similarly can you tell for: $\large \sqrt{9l_1^2} = ??$

23. Brianna9898

so you have to keep the 2 at the bottom

the one and two are sub scripts to differentiate between the first length and the second, thus, 1 and 2 respectively.

25. waterineyes

see, 1 and 2 is differentiating lengths of the two square you are given with, so don't think here of just l think here of $$l_1$$ and $$l_2$$..

26. Brianna9898

so it would be $9l _{1} ??$

27. waterineyes

You forgot to take square root of 9. \(l_1\0 is good though..

28. waterineyes

What is square root of 9?

29. Brianna9898

3

30. waterineyes

Yep after square root you will get like: $\large l_2 = 3 \times l_1$

31. waterineyes

So, which answer choice is this?

32. Brianna9898

the first one?

33. waterineyes

Well Done...

34. waterineyes

And give all the thanks to @Shadowys

35. Brianna9898

yayyy! thank you guys for helping me!

36. Brianna9898

I don't even know how to give a medal on this thing

37. waterineyes

Are you seeing best response after shadows post ?/ Just click that..

38. Brianna9898

oh okay, can I give a medal to two ppl?

39. waterineyes

No, just only one..

40. waterineyes

On one post you can give medal to one only..

41. Brianna9898

thanx for the medal @Shadowys !